Question: Solve: $\sqrt{x^2 + 5} - 1 = x$

Solution:
Given,

$\sqrt{x^2 + 5} - 1 = x$

$or, \sqrt{x^2 + 5} = x +1$

[ Squaring both sides ]

$or, (\sqrt{x^2 + 5} )^2 = (x +1)^2$

$or, x^2 + 5 = x^2 + 2x + 1$

$or, x^2 - x^2 + 5 - 1 = 2x$

$or, 0 +4 = 2x$

$or, 2x = 4$

$or, x = \dfrac{4}{2}$

$\therefore x = 2$
= Answer